Question

If cosB = `(1)/(3)` and ∠C = 90°, find sin A, and B and cot A.

Answer 1

cosB = `"Base"/"Hypotenuse" = "BC"/"AB"`

(AB)² = (AC)² + (BC)²
⇒ AC = `sqrt(("AB")^2 - ("BC")^2`
⇒ AC = `sqrt(3^2 - 1)`
= `sqrt(9 - 1)`
= `2sqrt(2)`

sin A = `"BC"/"AB" = "Perpendicular"/"Hypotenuse" = (1)/(3)`

tan B = `"AC"/"BC" = "Perpendicular"/"Base" = 2sqrt(2)`

cot A = `(1)/"tan A" = "BAse"/"Perpendicular" = "AC"/"BC" = 2sqrt(2)`.